__OPTICS__

__DR.RIGOL__

__REFRACTION ON A SPHERICAL SURFACE__

__REFRACTION ON A
SPHERICAL SURFACE:__

If we consider only the paraxial rays, when the light
incident parallel to the principal axes is refracted on a spherical surface ( with radius of curvature R), it will intercept the
principal axes in the focus.

The formula that relates the focus (f) of curvature with the
radius of curvature of the surface ® is :

Pay attention to the fact that the value of h doesn’t appear
in the formula, that means, the point of interception is independent of the
value of h. That is true, of course, only for paraxial rays. Now, it will be
ease to find the formula that relates the object distance, the image distance,

the radius of curvature with the indexes
of refraction n_{1} and n_{2}.

Using

Using the symbols defined in the graph, lets
get the expression for the formula for the refraction:

And this is the final result :

Which is the formula we find in the books.